A Model Relating Structure of Colloidal Gels to Their Elastic Properties

A scaling model relating the microscopic structure parameters of colloidal gels to their macroscopic elastic properties is proposed. This model allows one to estimate the fractal dimension in any gelation regime, purely based on rheological properties (storage modulus and limit of linearity), without resorting to other types of measurements. In particular, an appropriate effective microscopic elastic constant is introduced to account for the mutual elastic contributions of both inter- and intrafloc links. This leads to a new parameter, α ∈ [0,1], which indicates the relative importance of these two contributions. This parameter can be estimated from the rheological data, and its value determines the prevailing gel regime. The model is applied to 12 gelation systems reported in the literature and identifies three gelation regimes: strong-link (α = 0), weak-link (α = 1), and transition (0 < α < 1). For the first two regimes, the new model correctly reproduces the results from the model developed by Shih et al.1 However, for the transition regime, corresponding to α ∈ (0.4,0.7), the new model is the only one providing a physically sound interpretation of the experimental results.